薄壁圆环作为一种典型结构单元，即使在完全弹性情况下，其撞击刚壁后的恢复系数（COR）也显著小于1。针对不同工况下完全弹性圆环正撞击刚壁的过程进行数值分析，结果显示其恢复系数主要集中在0.76～0.8之间，个别工况下甚至更小。将完全弹性薄壁圆环等效成曲梁并进行微元分析，结合平衡方程和几何方程求解得到圆环在不同振动模态下的振型、频率等振动信息。结合数值模拟结果，分析指出在一定的材料参数和碰撞速度范围内，完全弹性薄壁圆环在撞击刚壁回弹过程中以一阶平动和二阶自由振动模态为主，恢复系数近似为一定值。
Abstract
As a kind of typical structural unit, after impacting against a rigid-wall, a thin-walled ring’s coefficient of restitution (COR) is significantly less than 1 under the condition of its full elasticity. The processes of the elastic ring impacting against the rigid-wall under different working conditions were analyzed numerically. The results showed that the ring’s COR is mainly concentrated within 0.76 ~ 0.8, this COR is more smaller under a certain working conditions. Then elastic ring was equivalent to a curved beam. A micro-element analysis was done for the curved beam. Combined with equilibrium equations and geometric equations, the ring’s vibration modal shapes and modal frequencies were solved. Combining with the numerical simulation results, is was shown that within a certain range of material parameters and impacting velocity, the full elastic ring mainly presents its 1st order translation mode and 2nd order free vibration mode in the process of its impacting against a rigid-wall, its COR keeps approximately a constant value.
关键词
弹性圆环 /
恢复系数 /
振动 /
模态分析
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Key words
elastic ring /
coefficient of restitution /
vibration /
modal analysis
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